find a polynomial function whose graph passes through the points (-1,8),(0,5),(1,6), and (2,17)
To find a polynomial function that passes through the given points, we can use the Lagrange interpolation formula.
Let's assume that the polynomial function is of degree 3, so it can be written as:
f(x) = ax^3 + bx^2 + cx + d
Using the Lagrange interpolation formula, we can write the function as:
f(x) = (8 * (x - 0)(x - 1)(x - 2) / ((-1 - 0) * (-1 - 1) * (-1 - 2)))
+ (5 * (x - (-1))(x - 1)(x - 2) / ((0 - (-1)) * (0 - 1) * (0 - 2)))
+ (6 * (x - (-1))(x - 0)(x - 2) / ((1 - (-1)) * (1 - 0) * (1 - 2)))
+ (17 * (x - (-1))(x - 0)(x - 1) / ((2 - (-1)) * (2 - 0) * (2 - 1)))
Simplifying this equation will give us the polynomial function:
f(x) = 3x^3 - 3x^2 + 4x + 5